In this page triangle worksheet solution4 we are going to see solution for each problems of the topic area of triangle worksheet.

(4) In each of the following, find the value of k for which the given points are collinear.

(i) (k,-1) ( 2 ,1) and (4,5)

**Solution:**

If the given points are collinear then the area of triangle is zero

(1/2) [(k + 10 – 4) – (-2 + 4 + 5k)] = 0

[(k + 6) – (2+ 5k)] = 0 x 2

(k + 6 – 2 - 5k) = 0

-4 k + 4 = 0

- 4k = -4

K = (-4)/(-4)

K = 1

Therefore the value of k is 1

(ii) (2,-5) ( 3 ,-4) and (9,k)

**Solution:**

If the given points are collinear then the area of triangle is zero

(1/2) [(-8 + 3k – 45) – (-15 - 36 + 2k)] = 0

[(3k - 53) – (-51+ 2k)] = 0 x 2

(3k - 53 + 51- 2k) = 0

k - 2 = 0

k = 2

Therefore the value of k is 2

(iii) (k,k) (2 ,3) and (4,-1)

**Solution:**

If the given points are collinear then the area of triangle is zero

(1/2) [(3k - 2 + 4k) – (2k + 12 - k)] = 0

[(7k - 2) – (k+12)] = 0 x 2

(7k - 2 – k - 12) = 0

6 k - 14 = 0

6k = 14

K = 14/6

K =7/3

Therefore the value of k is 7/3

triangle worksheet solution4 triangle worksheet solution4

- Section formula
- Area of quadrilateral
- Centroid
- Midpoint
- Distance between two points
- Distance between two points worksheet
- Slope of the line
- Equation of the line
- Equation of line using two points worksheet
- Equation of the line using point and slope worksheets
- Point of intersection of two lines
- concurrency of straight line
- Circumcentre of a triangle
- Orthocentre of a triangle
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- Locus
- Perpendicular distance
- Angle between two straight lines
- Equation of a circle
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- Equation of a circle passing though three points
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Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existe